A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at lease 200 calculators must be shipped each day.

Question

If each scientific calculator sold results in a $2 loss,but each graphing calculator produces a $5 profit, how many if each type should be made daily to maximize net profits?

A) Define the objective equation.
B)Define the constraint equations.
C)Graph the associated constraint equations.
D) Determine the vertices of each of the graphed equations.
E) Determine how many of each type of calculators should be made daily to maximize the net profits and the amount of net profit.

Answer 1

maximize p = -2x+5y subject to
x <= 200
y <= 170
x+y >= 200

looks like 30 scientific, 170 graphing

Answer 2

How did you get 30 and 170? If the equation is -2x+5y?

Answer 3

Well, just intuitively, if you lose money on each scientific calculator, you want to produce as few as possible. Ideally, zero.

Unfortunately, you have to produce at least 200 boxes a day, and can only produce 170 graphing calculators. So, you gotta do at least 30 of the losers.